Magnetic Order and Dynamics in an Orbitally Degenerate Ferromagnetic Insulator

Neutron scattering was used to determine the spin structure and the magnon spectrum of the Mott-Hubbard insulator ${\mathrm{Y}\mathrm{T}\mathrm{i}\mathrm{O}}_3$. The magnetic structure is complex, comprising substantial $G$-type and $A$-type antiferromagnetic components in addition to the predominant ferromagnetic component. The magnon spectrum, on the other hand, is gapless and nearly isotropic. We show that these findings are inconsistent with the orbitally ordered states thus far proposed for ${\mathrm{Y}\mathrm{T}\mathrm{i}\mathrm{O}}_3$ and discuss general implications for a theoretical description of exchange interactions in orbitally degenerate systems.

Figure 1

(a) Ferromagnetic and (b) $G$-type antiferromagnetic components of the ordered magnetic moment of ${\mathrm{Y}\mathrm{T}\mathrm{i}\mathrm{O}}_3$ extracted from the amplitudes of the $(0,2,0{)}_o$ and $(0,1,1{)}_o$ magnetic Bragg reflections, respectively. A weakly temperature dependent nuclear contribution to both reflections has been subtracted. The inset gives a pictorial representation of the magnetic structure. The ${\mathrm{T}\mathrm{i}\mathrm{O}}_6$ octahedra are highlighted.

Figure 2

Representative constant-$\mathbf{q}$ scans with (a) $\mathbf{q}=(\frac{1}{4},\frac{1}{4},0{)}_c$ and (b) $\mathbf{q}=(\frac{1}{2},\frac{1}{2},\frac{1}{2}{)}_c$ at 5 K ($<T_C$) and 50 K ($>T_C$). At 5 K both phonons and sharp magnons are present. The magnons become overdamped above $T_C$. The lines are results of a convolution of a magnon cross section with the spectrometer resolution function, as discussed in the text.

Figure 3

Spin wave dispersion relations at $T=5\mathrm{K}$. The solid symbols refer to magnetic excitations, whereas the open symbols can be identified as phonons. The grey points were extracted from scans at low temperatures, without a corresponding scan above $T_C$, so that an unambiguous identification is not yet possible. The solid line is the magnon dispersion relation derived from an isotropic Heisenberg model. The dashed line is the same model augmented by a spin anisotropy as discussed in the text.

Figure 4

Exchange constants (in units of $J_{\mathrm{S}\mathrm{E}}$) as a function of the Hund coupling $\eta$ for different values of the parameter $n_{xy}$ characterizing the orbital state. The inset shows the ratio of in-plane and out-of-plane exchange couplings for fixed $\eta$ as a function of $n_{xy}$.